Is anyone old enough to remember the ad in which two people walking down the street while snacking accidently bump into each other and discover peanut butter on a chocolate bar? Well, it turns out that when physics students run into each other on the street, the result is a quasicrystal with topological properties.

The students in question were members of two different labs in two different physics departments who were both out for a stroll on the same street in Tel Aviv – far from Rehovot and the Weizmann Institute. One was experimenting with a new kind of quasicrystalline optical system – thin optical fibers etched into glass that are arranged in quasicrystal fashion – ordered but non-periodic. The other was investigating a new class of materials called topological materials, in which the interior of the material is insulating but the surface conducts electricity. Some “shop talk” on their day off led them to realize that combining the two might help probe some unanswered questions.

A SEM figure of the etched waveguides composing the optical quasicrystal

These two were joined by another three students from the two departments, and the five embarked on an independent experiment. They created an optical quasicrystal and shined laser light through one optic fiber at a time. When light was shone through a middle fiber, it “hopped” across to the other fibers and exited through all of them. But if they passed the light through a fiber on just one of the edges, that light stayed on its edge without moving to the other fibers.

Even more wonderful and astonishing was the “adiabatic pump” they created. By varying the distances between one fiber and its neighbor along their lengths, they managed to get the beam of light to enter from one side and hop across the crystal, exiting from the opposite corner.

The explanation for this verges, to the uninitiated at least, on the magical: Those one-dimensional quasicrystals (the optic fibers) are a projection of a higher-dimensional system, and they preserve some of its properties. That means that if the same phenomenon can be found in two or three dimensions, these could be projections from systems of up to six dimensions.

An adiabatic light pump: (l) The setup: The spacing between the optic fibers is slowly varied to induce light pumping. (r) Measurements of the intensity distribution as the light moves down the quasicrystal show it crossing from right to left

Comments

The intensity distribution across the quasicrystal suggests that perhaps the light pump could be more efficient at lateral propagation (hopping) if the spacing between the fibers is made to be more regularly patterned from right-to-left. The spacing between each fiber still would not be constant along the length. Think of a series fibers with the same skewed S-curves, but the curve is displaced further along the long axis as you move to the next fiber on the left. The light entering on the right-most fibers is “bunched” at a curve. The curve is not yet reached in the fiber to its left, so it is favorable for the light to hop to the left fiber and “relax”.

It should also be possible to prepare a 3-D system by stacking planes of quasicrystals. The design could enable light propagation from specific entry points only along designed routes. It may be possible to have a variety of dimensions for the guides so that the 3-D block can discriminate and operate simultaneously with a variety of wavelengths.